Wiener model

This article deals with a model for nonlinear dynamical systems. For the accordion see Vienna model .

Block diagram of a Wiener model, which consists of the series connection of a linear system and a static non-linearity

The Wiener model (after the American mathematician Norbert Wiener ) is a special type of model for nonlinear dynamic systems . The characteristic is the structure, consisting of the series connection of a linear time-invariant dynamic system and a static non-linearity. In the Hammerstein model , the same elements are arranged in a different order.

The Wiener model is defined for both single-variable and multi-variable systems .

The Wiener model is generally used in control engineering, for example in modeling , system identification and controller design.

For single-variable systems, the mathematical description is

${\displaystyle {\tilde {u}}(t)=u(t)*g(t)}$

${\displaystyle y(t)=f({\tilde {u}})}$,

in which

• ${\displaystyle g(t)}$is the impulse response belonging to the transfer function of the linear system and ${\displaystyle G(s)}$
• ${\displaystyle *}$denotes the convolution operator .

See also

• Systems theory